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Subspace-Search Variational Quantum Eigen solver (SSVQE) is a searchingmethod of multiple states and relies on the unitarity of transformations toensure the orthogonality of output states for multiple states. Therefore, thismethod is thought to be a promising method for quantum chemistry becauseordinary Variational Quantum Eigen solver (VQE) can only calculate the excitedstates step by step from the ground state based on Variational Quantumdeflation (VQD). We compare the advantage of VQE, SSVQE with/without theconstraint term and/or Tabu search term, which is added by the Lagrangemultiplier method so as to calculate the desired energy levels. We evaluatedthe advantage by calculating each level of H2 and HeH, respectively. As theresimulation results, the accuracy calculated by constrained VQE with Tabu searchindicates higher accuracy than that of our other algorithm, for analysis on H2.The accuracy calculated by constrained SSVQE indicates higher that of theconstrained VQE with Tabu search. We found it is beneficial for enhancing theaccuracy to use constraint terms decreasing convergence times to use Tabusearch terms according to the nature of molecules. We demonstrate thatconstraint and Tabu search terms contribute to the accuracy and convergencetime on quantum chemical calculating.

Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver